Do all poems have to flow?

No, not all poems have the flow. Poems that flow are called traditional, and if you look around at different poems, you can see that not all of them are traditional.

An example of a non-flowing/non-traditional poem is:

Dreams

Dreams can be anything

Happy, sad

Exciting, boring

Triumphant, failure

Action, sedentary

Understood, confusion

Dreams can be anything

Long, short

Wide, narrow

Fat, skinny

Fast, slow

Black, white

Why look at what is and not what can be?